An object with a mass of #3 kg# is pushed along a linear path with a kinetic friction coefficient of #u_k(x)= e^x-2x+3 #. How much work would it take to move the object over #x in [3, 4], where x is in meters?

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Answer 1 · 2017-06-09T13:42:13

The work is #=897.1J#

The work done is

#W=F*d#

The frictional force is

#F_r=mu_k*N#

The normal force is #N=mg#

The mass is #m=3kg#

#F_r=mu_k*mg#

#=3(e^x-2x+3)g#

The work done is

#W=3gint_(3)^(4)(e^x-2x+3)dx#

#=3g*[e^x-2/2x^2+3x]_(3)^(4)#

#=3g((e^4-16+12)-(e^3-9+9))#

#=3g(e^4-e^3-4)#

#=3g(30.51)#

#=897.1J#